Fast and robust identification of railway track stiffness from simple field measurement

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We propose to combine a physics-based finite element (FE) track model and a data-driven Gaussian process regression (GPR) model to directly infer railpad and ballast stiffness from measured frequency response functions (FRF) by field hammer tests. Conventionally, only the rail resonance and full track resonance are used as the FRF features to identify track stiffness. In this paper, eleven features, including sleeper resonances, from a single FRF curve are selected as the predictors of the GPR. To deal with incomplete measurements and uncertainties in the FRF features, we train multiple candidate GPR models with different features, kernels and training sets. Predictions by the candidate models are fused using a weighted Product of Experts method that automatically filters out unreliable predictions. We compare the performance of the proposed method with a model updating method using the particle swam optimization (PSO) on two synthesis datasets in a wide range of scenarios. The results show that the enriched features and the proposed fusion strategy can effectively reduce prediction errors. In the worst-case scenario with only three features and 5% injected noise, the average prediction errors for the railpad and ballast stiffness are approximately 12% and 6%, outperforming the PSO by about 6% and 3%, respectively. Moreover, the method enables fast predictions for large datasets. The predictions for 400 samples takes only approximately 10 s compared with 40 min using the PSO. Finally, a field application example shows that the proposed method is capable of extracting the stiffness values using a simple setup, i.e., with only one accelerometer and one impact location.
Original languageEnglish
Article number107431
Pages (from-to)1-25
Number of pages25
JournalMechanical Systems and Signal Processing
Publication statusPublished - 2021


  • Field hammer test
  • Frequency response function
  • Gaussian process regression
  • Railway track stiffness
  • Structural identification


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